Research On The Efficiency And Cost Of Complex Networks

Recent years, the discovery of small-world and scale-free properties of many natural and artificial complex networks has stimulated a great deal of interest in studying various complex networks, which has led to complex networks attracting more and more attentions from various fields of science. At present, scientists have already done much research on lots of networks. For example, communication networks, computer networks, neuronal networks, social networks, scientific-collaboration networks, ecological networks, traffic networks, and so on. The aim of the studies on these networks is to investigate their mechanism, understand their developing rules, and find the relationship between their structure and the complex functioning processes on them, so as to accumulate the knowledge about the natural disciplinarians dominating the complex systems. As a branch of complexity science, the research for complex networks has drawn more and more attentions among scholars, and more progresses have been made both theoretically and practically.Complex networks describe a wide range of complex systems in nature and society, nodes represent the system element, and whose links stand for the interactions between them. This paper aims at the research on the efficiency and cost of complex network, at the same time, analyzes the topological structures of complex networks in detail, which is the base for the research on this paper. In this paper, the research background and development for complexity science and complex networks are introduced, and then several important topological parameters, several important complex network models and the major results recently achieved in the study of the structure and dynamics of complex networks are investigated at length, Lastly the influence of network efficiency and topological structures on the error and attack tolerance characteristics of complex networks is presented briefly. The main research work is as follows:1) For the first time the topological structure of China Railway Network (CRN) is investigated roundly, and some important topological parameters on CRN, like cumulativedegree distribution, cumulative probability distribution of the number of trains, cumulative probability distribution of the number of stations, cluster coefficient and path lengths, are obtained, and small world property of it is found. Furthermore some other important parameters on CRN like network efficiency, cost, and so on, are obtained, and its robustness and security are analyzed in detail. All these results are with potential theoretical value and practical significance for the construction and optimization of CRN.2) According to efficiency and cost, this paper does much research on the change of efficiency while increasing the cost to the random network, the small-world network, and the scale-free network. We have got the change law of the whole efficiency of these three kinds of complex networks in four different kinds of methods to increase the cost, including not adding node and random attachment, not adding node and preferential attachment, adding node and random attachment, adding node and preferential attachment. Thereby open out how to obtain the networks' maximum efficiency while increasing fixed costs, this will play an important part in improving lots of complex networks in society.